1 research outputs found
Divergence/connection preservation scheme in the curvilinear domain with a small geometric approximation error
Additional grid points are often introduced for the higher-order polynomial
of a numerical solution with curvilinear elements. However, those points are
likely to be located slightly outside the domain, even when the vertices of the
curvilinear elements lie within the curved domain. This misallocation of grid
points generates a mesh error, called geometric approximation error. This error
is smaller than the discretization error but large enough to significantly
degrade a long-time integration. Moreover, this mesh error is considered to be
the leading cause of conservation error. Two novel schemes are proposed to
improve conservation error and/or discretization error for long-time
integration caused by geometric approximation error: The first scheme retrieves
the original divergence of the original domain; the second scheme reconstructs
the original path of differentiation, called connection, thus retrieving the
original connection. The increased accuracies of the proposed schemes are
demonstrated by the conservation error for various partial differential
equations with moving frames on the sphere.Comment: 20 pages, 11 figure